The present invention relates generally to methods and apparatus for controllably positioning a solar concentrator and, more particularly, to methods and apparatus for controllably positioning a solar concentrator that take into account at least one of a gravitational residue error, azimuth transfer function, and elevation transfer function error and an error due to atmospheric refraction.
There is currently a large domestic and international market for clean non-polluting generated grid and remote electrical power, such as the electrical power generated by solar energy generating systems. This demand is anticipated only to grow. For example, over the next 12 years, the average growth of power consumption in California is estimated to be 700 MW per year, while Arizona consumers are anticipated to demand an additional 200 MW per year between the years 2000 and 2010. In addition, the state of Nevada has one of the fastest growing energy needs per capita in the United States with its electrical needs estimated to grow in excess of 200 MW per year. In the solar belt states alone, the estimated growth is anticipated to be more than 1000 MW per year. Furthermore, an estimate by the World Bank of the international electrical market in the solar belt countries is for growth of more than 2000 MW year.
Of this growth in power consumption, at least a portion will be solar energy. For example, the state of Arizona has decreed that 1% of all generated electrical power must be solar generated. This requirement creates the need for 350 MW of grid electricity in this state from solar energy alone. Other states in the solar belt, such as California, Nevada, New Mexico, etc., have or are expecting similar legislation.
A variety of solar-to-electrical energy conversion systems have been developed with the most cost-effective systems being concentrating solar energy systems that focus the energy of the sun to a relatively small area. One exemplary concentrating solar energy system is a Stirling dish developed by McDonnell Douglas Corporation. A Stirling dish includes a plurality of reflective facets disposed side-by-side upon a support frame to define a reflective surface. The reflective surface typically has a parabolic or spherical shape. The parabolic reflective surface of the Stirling dish concentrates the incident solar energy upon a power conversion unit that is located at the focal point of the reflective surface. In this regard, the power conversion unit is generally mounted upon the distal end of a support arm that extends forwardly of the Stirling dish. The support frame that carries the plurality of reflective facets and the support arm that carries the power conversion unit are mounted upon a pedestal which, in turn, is secured to a foundation within the earth. The pedestal permits the Stirling dish to move in both an azimuth rotational plane and an elevation rotational plane such that the Stirling dish can track the sun throughout the day. Thus, the Stirling dish also generally includes an azimuthal drive and an elevational drive, including an elevation activator, for providing the desired movement in response to azimuth and elevation commands issued by a controller or the like. Typically, these commands attempt to drive one Stirling dish to a position at which a centerline defined by the reflective surface is aligned with the sun. Other types of concentrating solar energy systems exist, however, including heliostats and other sun tracking solar concentrators.
There are two general types of tracking control systems for use with concentrating solar energy systems, namely, open loop and closed loop control systems. In a closed loop tracking control system, a sun sensor is aligned to the centerline defined by the reflective surface. As such, the sun sensor generates error signals between the centerline of the reflective surface and the line-of-sight to the sun, i.e., the sun reference vector. While closed loop tracking control systems can be effective, closed loop tracking control systems are generally quite expensive due to the addition of a sun sensor and the attendant cabling, additional interface electronics and increased operational and maintenance costs attributable to the additional hardware. Further, closed loop tracking control systems have difficulty maintaining track during periods of cloud cover. In this regard, if the reflective surface is not pointing at the sun when the sun comes out from behind the clouds, the concentrating solar energy system may be damaged. As such, open loop tracking commands must be calculated during the period of time in which the sun is behind the clouds. Additionally, further problems arise in instances in which the face or lens of the sun sensor becomes dirty, such as from dust, sand or other airborne particles. In this regard, a sun sensor relies upon the shading of the solar cells to obtain an error voltage. As such, a sun sensor having a dirty lens will unevenly illuminate the solar cells which, in turn, creates tracking errors and also loss of track during low sun irradiance levels. Closed loop tracking control systems also suffer from an additional cost of aligning the sun sensor to the centerline defined by the reflective surface and maintaining this alignment over time. Furthermore, the sun sensor oftentimes serves as a roosting place for birds which can cause additional problems, by altering the alignment of the sun sensor or soiling the lens of the sun sensor. As such, most concentrating solar energy systems utilize an open loop tracking control system.
In an open loop tracking control system, the position of the sun is calculated by a set of ephemeris equations. The reflective surface is then commanded to point toward the position of the sun. As a result of the open loop nature of this system, there is no feedback from the solar concentrator that the reflective surface is actually pointing at the sun. Unfortunately, the command coordinate system, i.e., the coordinate system in which the commands that direct the position of the solar concentrator are formulated, and the concentrator coordinate system, i.e., the actual coordinate system defined by the physical construction of the solar concentrator, are generally somewhat misaligned. As such, the centerline defined by the reflective surface may not be pointing directly at the sun even though commands have been issued that would have caused the reflective surface to point at the sun if the concentrator coordinate system and the command coordinate system were identical. Typical sources of error that will cause the misalignment of the command coordinate system and the concentrator coordinate system are pedestal/foundation tilt errors, elevation pivot point manufacturing tolerances, azimuth and elevation reference errors, gravity bending of the structure, atmospheric bending of the sun rays, reflectivity surface misalignment errors, elevation actuator offset errors and errors inherent in the mathematical model utilized by the control system.
The deleterious effect of these errors can be reduced by increasing the manufacturing tolerances and the installation tolerances. However, the increase in these tolerances will greatly increase the cost of a concentrating solar energy system such that the resulting concentrating solar energy system will no longer be economically competitive with either non-concentrating solar systems or conventional power systems. The deleterious effect of these errors can also be reduced by modifying the pointing commands that position the reflective surface in an attempt to compensate for the misalignment errors.
In this regard, some concentrating solar energy systems automatically provide a fixed bias of correction in the azimuth direction and a fixed bias of correction in the elevation direction. While the application of a fixed amount of error correction is somewhat helpful, the azimuth and elevation errors vary throughout the day and year as the position of the sun and the solar concentrator changes. In this regard, FIGS. 1A and 1B depict the elevation and azimuth track errors in degrees as a function of azimuth position in degrees from due south. In this regard, both the azimuth and elevation track errors vary by about 0.6 degrees such that incorporation of a fixed correction value, such as an average error correction value, would still subject the concentrating solar energy system to a substantial amount of uncorrected error in both the azimuth and elevation rotational planes.
In order to take into account variations in the azimuth and elevation errors throughout the day, one system manually determines the errors attributable to azimuth tilt and gravity bending. To determine the errors attributable to azimuth tilt, a leveling device, such as an inclinometer, is placed on the upper part of the rotating structure, i.e., the structure that rotates about the pedestal, and the angle is noted. The solar concentrator is then rotated between five and ten degrees and the tilt angle is again measured. This process is repeated in relatively small steps until the solar concentrator is rotated through 360 degrees. The data is then plotted and the tilt parameters are estimated from the plotted data. Similarly, the errors attributable to gravity bending are determined by mounting an inclinometer on the elevation rotating part of the solar concentrator, i.e., the structure above the elevation pivot point. The solar concentrator is then commanded to an angle and the actual angle is measured with the inclinometer. The solar concentrator is then commanded to another elevation angle which is between about five and ten degrees greater than the initial elevation angle. This process is continued until measurement data has been obtained for elevation angles from 0 degrees to 90 degrees. The measured angles are then subtracted from the commanded elevation angles to obtain the error attributable to gravity bending. This data is then curve fit as a function of the elevation angle and the resulting curve is utilized to adjust the commanded elevation angle in order to correct for errors attributable to gravity bending.
While this technique takes into account the variations in the errors attributable to azimuth tilt and gravity bending throughout the day, this technique does not recognize that these errors, as well as the other errors to which the solar concentrator is subjected, vary not only throughout the day, but also from day to day and season to season as the relative position of the sun in the sky changes. Additionally, this technique only takes into account two tracking errors, namely, errors attributable to azimuth tilt and errors attributable to gravity bending, thereby ignoring the effects of a number of other error sources, such as azimuth reference error, errors attributable to reflective surface non-orthogonality, elevation reference position error, elevation rotational tilt errors and the like. Moreover, this technique requires substantial manual labor in the field in order to collect the necessary data.
Another technique for measuring the misalignment errors and for modifying the pointing commands is described by U.S. Pat. No. 4,564,275 to Kenneth W. Stone, the contents of which are incorporated herein in their entirety. This technique automatically aligns one or more heliostats by comparing the actual sun beam centroid position to a command reference position to determine the error in the sun beam centroid location. This is done several times over the day depending upon the required accuracy. The sun beam centroid position error is then analyzed to correlate the error to errors in the track alignment system of the heliostat. In this regard, the technique described by U.S. Pat. No. 4,564,275 takes into account errors attributable to the non-orthogonality of the facets of the reflective surface, errors in the elevation and azimuth reference positions and errors in the azimuth rotational tilt. Based upon the errors, the command reference position is updated to automatically correct for the errors. While the technique described by U.S. Pat. No. 4,564,275 represents a substantial improvement in open loop tracking control systems for solar concentrators, it would be desirable to further improve the open loop tracking control system in order to even more accurately align the centerline defined by a reflective surface with the sun reference vector, thereby capturing a greater percentage of the energy delivered by the sun and increasing the efficiency of the concentrating solar energy system.
A method, apparatus, control system and computer program product are provided for controllably positioning the solar concentrator. Advantageously, the various embodiments of the present invention determine the respective errors generated by more and different error sources than prior techniques, including error sources selected from the group consisting of a gravitational residue error, an elevation transfer function error and an error attributable to atmospheric refraction. Based upon the respective errors, the various embodiments of the present invention determine an elevation command and an azimuth command to compensate for the vertical error and the horizontal error between the centerline of the solar concentrator and the sun reference vector such that the solar concentrator can be more precisely positioned, thereby improving the efficiency with which the solar concentrator collects solar energy.
According to one embodiment of the present invention, a control system is provided for positioning a solar concentrator. The control system includes an input section for receiving signals representative of the vertical error and the horizontal error between the centerline of the solar concentrator and the sun reference vector. In one embodiment, the input section repeatedly receives signals representative of the vertical error and the horizontal error at a plurality of different times throughout the day such that the solar concentrator can be repositioned throughout the day as necessary to optimize its collection of the solar energy. The control system also includes a processing element for determining the elevation command and the azimuth command to compensate for the vertical error and the horizontal error. In one advantageous embodiment, the processing element is comprised of a computer program product having a computer-readable storage medium with computer-readable program code embodied therein for performing the various functions of the processing element. However, the processing element can be embodied in other manners, if so desired.
Regardless of its physical embodiment, the processing element determines respective errors generated by a plurality of error sources that contribute to the vertical error and/or the elevation error. According to the present invention, the plurality of error sources include at least one error source selected from a group consisting of a gravitational residue error, an elevation transfer function error and an error due to atmospheric refraction. In one embodiment, the processing element determines the respective errors by collectively determining a gravitational residue error g, an elevation transfer function error e and an error due to atmospheric refraction. The processing element can also determine additional errors by individually determining each of a first azimuth rotational tilt error xcex31, a second azimuth rotational tilt error xcex32, a first elevation rotational tilt error xcfx86, a second elevation rotational tilt error xcex41 and a reflective surface non-orthogonality error xcex42.
The processing element also determines the elevation command and the azimuth command at least partially based upon the respective errors generated by the plurality of error sources. In one advantageous embodiment, the processing element determines the elevation command by determining an elevation command angle xcexa8c as follows: xcexa8c sinxe2x88x921(sin xcex31 cos xcexa8r cos "PHgr"rxe2x88x92sin xcex32 cos xcexa8r sin "PHgr"r+sin xcexa8r )xe2x88x92dxcexa8 wherein xcex31 and xcex32 are azimuth rotational tilt errors, "PHgr"r and xcexa8r are elevation and azimuth angles, respectively, in an inertial reference system that are required to align the centerline of the solar concentrator and a sun reference vector, and dxcexa8 is a combination of the elevation transfer function error, the gravitational residual error, and the error due to atmospheric refraction.
Likewise, the processing element of this advantageous embodiment preferably determines the azimuth command by determining an azimuth command angle "PHgr"c as follows:       Φ    c    =                    cos                  -          1                    ⁡              [                                            A              ⁢                              xe2x80x83                            ⁢              C                        +            BD                                              A              2                        +                          B              2                                      ]              -          Φ      e      
wherein A, B, C and D are defined as follows:
A=cos xcex cos xcex42 
B=cos xcex41 sin xcex42xe2x88x92sin xcex41 cos xcex42 sin xcex
C=cos xcex31 cos xcexa8r cos "PHgr"rxe2x88x92sin xcex31 sin xcexa8r
D=sin xcex31 sin xcex32 cos xcexa8r cos "PHgr"r+cos xcex32 cos xcexa8r sin "PHgr"r+sin xcexa8r cos xcex31 sin xcex32 
wherein xcex is defined as follows:
xcex=xcexa8cxe2x88x92xcexa8e+g(xcexa8c)+e(xcexa8c)+r(xcexa8c) 
wherein xcexa8c is an elevation command angle, xcexa8e is an elevation reference position error, g(xcexa8) is a gravitational residue error, e(xcexa8) is an elevation transfer function error and r(xcexa8) is an error due to atmospheric refraction, and wherein xcex41 is an elevation rotational tilt error, xcex42 is a reflective surface non-orthogonality error, xcex31 and xcex32 are azimuth rotational tilt errors and "PHgr"r and xcexa8r are elevation and azimuth angles, respectively, in an inertial reference system that are required to align the centerline of the solar concentrator and a sun reference vector.
The control system also includes an output section for providing signals representative of the elevation command and the azimuth command. The elevation command and the azimuth command can then be utilized to controllably position the solar concentrator to compensate for the vertical error and the horizontal error between the centerline of the solar concentrator and sun reference vector.
According to another aspect of the present invention, an apparatus for controllably positioning the solar concentrator is provided that includes a measurement system for determining the vertical error and the horizontal error between the centerline of the solar concentrator and the sun reference vector, a processing element as described above in conjunction with the control system, and a positioning mechanism for positioning the solar concentrator based upon the elevation command and the azimuth command in order to compensate for the vertical error and the horizontal error.
The measurement system may be either a sun sensor or a digital image radiometer. Alternatively, the measurement system may be adapted to move the solar concentrator from a nominal position to an aligned position at which the difference between the gas temperatures of each quadrant of the solar concentrator is minimized. Based upon the horizontal and vertical distances that the solar concentrator is moved from the nominal position to the aligned position, the measurement system of this embodiment can determine the horizontal and vertical errors, respectively. In yet another embodiment, the measurement system may be adapted to move the solar concentrator from a nominal position to an aligned position at which the maximum power factor is obtained. According to this embodiment, the measuring system is further adapted to determine the horizontal and vertical distances that the solar concentrator is moved from the nominal position to the aligned position in order to determine the horizontal and vertical errors, respectively.
According to another aspect of the present invention, a method of controllably positioning the solar concentrator is provided. In this regard, the method initially determines the vertical and horizontal errors between the centerline of the solar concentrator and the sun reference vector. The method then determines an elevation command and an azimuth command to compensate for the vertical and horizontal errors, respectively. In this regard, the method initially determines respective errors generated by a plurality of error sources that contribute to one or more of the vertical and horizontal errors. As described above, the plurality of error sources include at least one of the gravitational residue error g, the elevation transfer function error e and the error r due to atmospheric refraction. The elevation command and the azimuth command are then determined based at least in part upon the respective errors generated by the plurality of error sources. Based upon the elevation command and the azimuth command, the solar concentrator can be positioned to compensate for the vertical and horizontal errors.
By taking into account the errors generated by a number of error sources including error sources not previously considered by open loop tracking control systems and methods, such as the gravitational residue error g, the elevation transfer function error e and the error r due to atmospheric refraction, the method, apparatus, control system and computer program product of the present invention can more precisely position the solar concentrator such that the centerline of the solar concentrator is aligned with the sun reference vector. As such, the efficiency with which the solar concentrator collects the solar energy is improved. By repeating this process at a number of different times throughout the day, various embodiments of the present invention can repeatedly optimize the performance of the solar concentrator throughout the day to obtain much better performance than conventional systems that utilize the same average correction factor throughout the entire day everyday. Still further, by implementing much of the functionality of the open loop control methodology of the present invention in software, the resulting apparatus is competitive in cost with conventional systems and can be readily reconfigured, if necessary.